The ability to flip the differential conductance between low and high values by
tuning some external parameter is of tremendous practical importance in molecular electronics
for switching device applications. Recently a topological quantum phase transition has been found in
a spin-1 Kondo model with two degenerate channels and single-ion magnetic anisotropy,
in which the zero-bias differential
conductance and the spectral density at zero temperature jump from their maximum possible values
to zero as the longitudinal single-ion anisotropy \(D\)  is increased beyond a threshold
value \(D_c\)  [1]}, [2]}.
By generalizing the theory of such topological transitions to nonequivalent channels and finite magnetic
field, we have for the first time conclusively identified FePc/Au(111) as an experimental realization of
this phenomenon, since our approach provides a unified description of the totality of experimental
observations.
The main difficulty in this identification is that for
\(D>D_c\)  the system is an unconventional Fermi liquid that cannot be adiabatically
connected to a non-interacting system by turning off the interactions
[1]}, [2]}, [5]}, [6]}. The corresponding concept of a non-Landau Fermi
liquid (NLFL) remains largely unfamiliar to most of the physics community. In the NLFL, the
Friedel sum rule has to be generalized by introducing a topological quantity that has been
previously overseen, even though it leads to a dramatic drop in spectral density and
differential conductance for \(D>D_c\) .
